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A317138 Numbers k such that (2k)^3 - 1 is a semiprime.

%I A317138 #22 Sep 08 2022 08:46:22
%S A317138 3,4,6,7,10,12,19,27,31,40,45,55,69,75,82,84,96,97,136,139,157,166,
%T A317138 174,199,201,217,250,286,321,322,360,364,381,399,406,430,432,439,460,
%U A317138 496,510,511,535,546,549,559,565,591,601,615,630,654,717,720,724,727,742
%N A317138 Numbers k such that (2k)^3 - 1 is a semiprime.
%C A317138 Numbers k such that 2k - 1 and 4k^2 + 2k + 1 are both prime.
%H A317138 K. D. Bajpai, <a href="/A317138/b317138.txt">Table of n, a(n) for n = 1..9443</a>
%F A317138 a(n) = A096175(n)/2 = (1/2)*(A242262(n) + 1)^(1/3).
%e A317138 From _K. D. Bajpai_, Nov 16 2019: (Start)
%e A317138 a(3) = 6 is a term because (2*6)^3 - 1 = 1727 = 11*157, which is a semiprime.
%e A317138 a(4) = 7 is a term because (2*7)^3 - 1 = 2743 = 13*211, which is a semiprime.
%e A317138 9 is not in the sequence because (2*9)^3 - 1 = 5831 = 7*7*7*17, which is not semiprime.
%e A317138 (End)
%p A317138 issp:= n-> not isprime(n) and numtheory[bigomega](n)=2:
%p A317138 select( n-> issp((2*n)^3-1),  [seq(n, n=1..200)]); # _K. D. Bajpai_, Nov 16 2019
%t A317138 Select[Range@ 750, PrimeOmega[(2 #)^3 - 1] == 2 &] (* _Michael De Vlieger_, Aug 02 2018 *)
%o A317138 (PARI) for(k=1,500,if(bigomega((2*k)^3-1)==2,print1(k,", ")))
%o A317138 (Magma) IsSemiprime:=func<i | &+[d[2]: d in Factorization(i)] eq 2>; [n: n in [2..800] | IsSemiprime(s) where s is (2*n)^3-1]; // _Vincenzo Librandi_, Aug 04 2018
%Y A317138 Cf. A096175, A242262.
%Y A317138 Cf. A237037 (numbers k such that (2k)^3 + 1 is a semiprime).
%K A317138 nonn
%O A317138 1,1
%A A317138 _Jianing Song_, Aug 01 2018